Grain boundary strengthening of FCC polycrystals
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Grain boundary strengthening of FCC polycrystals R. Arturo Rubio1, Sarra Haouala1, Javier LLorca2,a) 1
IMDEA Materials Institute, Getafe, Madrid 28906, Spain IMDEA Materials Institute, Getafe, Madrid 28906, Spain; and Department of Materials Science, Polytechnic University of Madrid, Madrid 28040, Spain a) Address all correspondence to this author. e-mail: [email protected] 2
Received: 30 November 2018; accepted: 30 January 2019
The effect of grain size on the flow strength of FCC polycrystals was analyzed by means of computational homogenization. The mechanical behavior of each grain was dictated by a dislocation-based crystal plasticity model in the context of finite strain plasticity and takes into the account the formation of pile-ups at grain boundaries. All the model parameters have a clear physical meaning and were identified for different FCC metals from dislocation dynamics simulations or experiments. It was found that the influence of the grain size on the flow strength of FCC polycrystals was mainly dictated by the similitude coefficient K that establishes the relationship between the dislocation mean free path and the dislocation density in the bulk. Finally, the modeling approach was validated by comparison with experimental results of the effect of grain size on the flow strength of Ni, Al, Cu, and Ag.
Introduction Plastic deformation of metallic alloys is controlled by dislocation motion, and the strategies to increase the flow stress are always based in the introduction of obstacles to dislocation slip. Reducing the grain size in polycrystals is an obvious choice, and Hall [1] and Petch [2] reported a phenomenological relationship for different metallic alloys between the yield g , of the form, stress, ry, and the average grain size, D 0:5 ry ¼ r‘ þ CHP D g
;
ð1Þ
where r∞ is the yield stress of a polycrystal with a very large grain size and CHP is a material constant. Further experimental data as well as theoretical investigations confirmed the increase in yield strength when the grain size was reduced although the experimental data were better approximated when the influence x of grain size was introduced as D g with 0.5 # x # 1 [3, 4, 5, 6]. From the physical viewpoint, the presence of grain boundaries influences the dislocation motion and dislocation storage because slip transfer is not possible across most grain boundaries due to the misorientation of the slip planes, leading to the formation of dislocation pile-ups [7, 8, 9]. The back-up stress induced by the pile-ups increases the critical resolved shear stress necessary to nucleate and move dislocations within the grain. Another implicit outcome of the misorientation between
ª Materials Research Society 2019
grain boundaries is the generation of geometrically necessary dislocations near the grain boundaries due to the anisotropy of the plastic deformation in each grain within the polycrystal. They account for the deformation incompatibility between grains with different orientations, and these additional dislocations also contribu
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